1. **State the problem:** Simplify the expression $$\frac{1}{6} + \frac{1}{3} + 2 \frac{1}{2}$$ to its simplest form. 2. **Convert mixed number to improper fraction:** $$2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$$ 3. **Find a common denominator:** The denominators are 6, 3, and 2. The least common denominator (LCD) is 6. 4. **Rewrite each fraction with denominator 6:** $$\frac{1}{6} = \frac{1}{6}$$ $$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$$ $$\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}$$ 5. **Add the fractions:** $$\frac{1}{6} + \frac{2}{6} + \frac{15}{6} = \frac{1 + 2 + 15}{6} = \frac{18}{6}$$ 6. **Simplify the fraction:** $$\frac{18}{6} = \frac{\cancel{18}}{\cancel{6}} = 3$$ **Final answer:** $$3$$